This invention relates to transmitting a stream of information bits by sending a corresponding sequence of signals over a channel in a plurality of signaling slots.
In typical so-called uncoded communication systems, the Q information bits appearing in a signaling slot are used to select a signal point from a two-dimensional (2D) constellation having 2.sup.Q signal points. The choice of the signal point to be sent in a given signaling slot is unrelated to the choice of the signal points to be sent in other signaling slots. The receiver estimates which signal point was sent by simply finding the nearest 2D signal point to the received, noise altered signal. The immunity of such a system to noise depends on the minimum distance between any two signal points in the 2D constellation.
Various techniques have been developed for improving the noise immunity of such systems.
For example, in so-called convolutionally coded systems of the type disclosed in Csajka et al., U.S. Pat. No. 4,077,021, and Ungerboeck, "Channel Coding with Multilevel/Phase Signals," IEEE Transactions on Information Theory, Vol. IT-28, pp. 55-67, January, 1982, the 2D constellation is doubled in size to include 2.sup.Q+1 signal points. a convolutional coder in the transmitter adds a redundancy bit to the Q information bits appearing in a signaling slot and the resulting Q+1 bits are used to select a signal point to be sent. The 2.sup.Q+1 signal points in the 2D constellation are partitioned into equal-sized subsets which have the property that the minimum distance between any two signal points in a subset is larger than the minimum distance between any two signal points in the constellation.
The convolutional coder is arranged so that the signal points to be sent are respectively drawn only from certain allowed sequences of subsets. The receiver estimates the sequence of sent signal points as those signal points from an allowed sequence of 2D subsets that are nearest (in the aggregate) to the sequence of received, noise altered signals. The immunity of such a convolutionally coded system to noise depends on the minimum distance between any two allowed sequences of 2D points. Because the minimum distance is larger than that of an uncoded system, a coding gain results. One cost of the system is that the size of the 2D constellation is doubled, offsetting some of the coding gain.
In the Csajka and Ungerboeck scheme, decoding is by means of the Viterbi algorithm described in Forney, "The Viterbi Algorithm", Proc. IEEE, Vol. 61, pp. 268-278, March, 1973, incorporated herein by reference.
Wei, "Rotationally Invariant Convolutional Channel Coding with Expanded Signal Space--Part I: 180.degree. and Part II: Nonlinear Codes", IEEE Journal on Selected Areas in Communications, Vol. SAC-2, pp. 659-686, September, 1984, describes convolutionally coded systems of the Csajka and Ungerboeck type that are capable of differential encoding for immunity to rapid carrier phase changes.
In so-called block coded systems (for example, those systems disclosed in Forney, U.S. patent application Ser. No. 485,069, filed Apr. 14, 1983, and now U.S. Pat. No. 4,597,090 issued 6-24-86, assigned to the same assignee as this application, and incorporated herein by reference) the information bits appearing in a block of more than one signaling slot are used to select a multi-dimensional signal point from a multi-dimensional constellation for transmission. A multi-dimensional constellation can be conceived as a concatenation of a number of constituent 2D constellations, the number being the number of signaling slots in a block. A multi-dimensional signal point is a concatenation of constituent 2D signal points, one from each constitutent 2D constellation. (In this respect, concatenating constituent signal points means assembling the coordinates of the respective constituent signal points as coordinates of a multi-dimensional signal point; concatenating constituent constellations means concatenating the respective signal points of the constituent constellations.) Certain dependencies exist between the constituent 2D signal points of a multi-dimensional signal point selected for a block. A coding gain results from those dependencies. However, no dependency exists between the two multi-dimensional signal points selected for any two blocks of signaling slots.
Multidimensional, convolutionally coded systems have also been proposed in which dependencies do exist between the multi-dimensional signal points selected for different blocks.
One such system is proposed in Gallager, U.S. patent application Ser. No. 577,044, filed Feb. 6, 1984, assigned to the same assignee as this application, and incorporated herein by reference.
Gallager shows a four-dimensional (4D) convolutionally coded system that uses a 240 signal point rectangular constituent 2D constellation to send 7 information bits per signaling slot. The 2D constellation is partitioned into four subsets. In Gallager the 14 information bits appearing in each block of two signaling slots are expanded (by a rate 3/4 8-state convolutional coder) to 15 selection bits used to select a 4D signal point in a 4D constellation. The 4D constellation is a concatenation of two 240 signal point constituent 2D constellations and is partitioned into 16 4D subsets each of which is a concatenation of two of the 2D subsets. (A 4D subset is a concatenation of two 2D subsets if every 4D point in the 4D subset is a concatenation of two 2D points from those two 2D subsets respectively). The signal point selection bits include four subset selection bits that are associated with 4D subsets in such a way that the Hamming distance between the allowed sequences of subset selection bits is indicative of the minimum squared distance between allowed sequences of 4D signal points. Gallager differentially encodes the bits fed to the convolutional coder in order to accomplish transparency to channel-induced phase rotations of 180.degree..
Another 4D convolutionally coded system is disclosed in Fang and Lee, "Four-Dimensionally Coded PSK Systems for Combatting Effects of Severe ISI and CCI", Globecom, 1983, pp. 1032-1038. They use a 2.sup.Q+1 signal point circular constituent 2D constellation to send Q information bits per signaling slot. The 4D constellation is a concatenation of two 2.sup.Q+1 signal point circular constituent 2D constellations. 2.sup.2Q+1 out of 2.sup.2Q+2 possible 4D signal points are selected for transmission. The selection is made such that the minimum distance between any two selected 4D signal points is maximized. The 2.sup.2Q+1 selected 4D signal points are partitioned into equal-sized subsets such that the minimum distance between any two 4D signal points in a subset is larger than that between any two selected 4D signal points. The partitioning is made directly on the 4D constellation without referring to a partitioning of the constituent 2D constellations. A convolutional coder of up to eight states is used to expand the 2Q information bits appearing in each block of two signaling slots to 2Q+1 selection bits to select a 4D signal point.
Another 4D convolutionally coded system is disclosed in Wilson and Sleeper, "Four-Dimensional Modulation and Coding: An Alternate to Frequency Reuse", NASA Report, UVA/528200/EE83/107, September, 1983. Their 4D constellation is taken from a 4D lattice (i.e., a regular arrangement of signal points) used for a block coded system. The partitioning of the 4D constellation into subsets is done directly without referring to a partitioning of the constituent 2D constellations. Preliminary investigations on the design of convolutional codes with four states or less are made for Q up to 2.